Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
432 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23770303 | C2 | semidirect |
| 4. #23761401 | C2 | semidirect |
| 5. #23761400 | C2 | semidirect |
| 6. #23761347 | C2 | semidirect |
| 205. C79 | #12150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23770303 | 2 |
| #23764648 | 2 |
| #23762386 | 2 |
| #23761401 | 2 |
| #23761400 | 2 |
| #23761347 | 2 |
| C79×#1607 | 2 |
| #12150 | 79 |